> geoffrey-ducournau — resume

Geoffrey Ducournau, PhD

R&D Researcher & AI Architect @ Dimtech

Research Affiliate @ Tsinghua University

Publications

// working paper · 2026

The Microdiffusion: Book-State Price Risk and Heavy Tails in Event Time

Evidence from the Qatar Stock Exchange

Geoffrey Ducournau · Dimtech · Tsinghua University (SEM)
Yibo Wang · Dimtech · Sorbonne University
Jinliang Li · Tsinghua University (SEM) · corresponding author

The visible limit order book is usually read as a signal of where the price will go next. This paper asks what it says about how far the price may go, in either direction. Using tick-by-tick data from the Qatar Stock Exchange, we estimate the microdiffusion, the conditional variance of the next mid-price move as a function of the quoted spread and the best-level imbalance, and we model the distribution of the move around that scale with a symmetric Generalized Hyperbolic innovation. The result is a conditional-variance and tail-risk model whose inputs are observable at the moment the forecast is made: the link between book state and scale is estimated from historical state and return pairs, so the current book conditions the forecast rather than revealing it outright.

The estimated state-to-variance map is partially reproducible out of sample. Its ranking of book states persists on held-out days, the spread-driven level transfers across days, instruments, and volatility regimes, and the imbalance dimension raises conditional variance contemporaneously but transfers weakly as a shape. A nested comparison under strict forecast losses sharpens this division: the quoted spread carries essentially all of the one-step predictive content, both for the probability that the price moves at all and for the size of the move when it does. The heavy-tailed innovation then matters where variance models are weakest: it materially improves extreme-tail coverage in intraday value-at-risk backtests, and the model's predictive log score is statistically indistinguishable from a jointly estimated GARCH-t benchmark while clearly improving on its Gaussian version.

MicrodiffusionMicropriceMicrostructureVolatilityDiffusionKurtosisRisk
Δxn=bx(In,Sn)+axx(In,Sn)ηn,Δn=1\boxed{\,\Delta x_n = b_x(I_n,S_n) + \sqrt{\axx(I_n,S_n)}\,\eta_n\,},\qquad \Delta n = 1

event-time stochastic equation for the mid-price move

axx(I,S)=Var ⁣(ΔxnIn=I, Sn=S)\axx(I,S) = \Var\!\left(\Delta x_n \given I_n=I,\ S_n=S\right)

the microdiffusion: conditional variance of the next move

E ⁣[(Δxn)2In=I, Sn=S]=axx(I,S)+bx(I,S)2\E\!\left[(\Delta x_n)^2 \given I_n=I,\ S_n=S\right] = \axx(I,S) + b_x(I,S)^2

event-time mean-square decomposition used for estimation

The microdiffusion surface and its out-of-sample transfer
Fig 1. The microdiffusion surface a​xx(I,S) and its out-of-sample transfer. (a) The estimated microdiffusion over the imbalance–spread grid (log-10 colour scale): conditional variance of price moves rises sharply toward wide spreads and varies with imbalance. (b) Out-of-sample calibration of the training map against held-out realised cell mean-square (rank correlation 0.82); the within-instrument transfer reported in the text is 0.48 (placebo 0.00).
Heavy-tailed innovation: density and tail exceedance of standardised residuals
Fig 2. Density (a) and tail exceedance (b) of the standardised residuals, with best-fit Gaussian, Student-t, and Generalized Hyperbolic innovations. The Generalized Hyperbolic follows the data closely; the Gaussian fails in the tail and the Student-t mis-sets it.
Intraday value-at-risk backtest on held-out sessions
Fig 3. Intraday VaR backtest on held-out QSE sessions, α ∈ {0.01, 0.05}. (a) Violation rates across instruments for the GH and Gaussian VaR. (b) Kupiec p-values, GH vs Gaussian; points above the diagonal favour GH. The GH model halves the median far-tail violation rate (0.0133 vs 0.0275 at α = 0.01).

This is a working paper. The full PDF is available on request — the replication code is public on GitHub.